The disclosure of Japanese Patent Application No. HEI 10-309920 filed on Oct. 30, 1998 and No. HEI 11-223755 filed on Aug. 6, 1999, each including the specification, drawings and abstract, is incorporated herein by reference in its entirety.
1. Field of the Invention
The present invention relates to analysis of a forging process of a material and, more specifically, to a technology for analyzing and/or predicting deformation of a workpiece caused due to the forging process performed thereon by setting fiber flow lines in the interior of the workpiece and calculating displacements of the fiber flow lines caused by the forging process. The invention relates particularly to a technology capable of analysis taking three-dimensional information into account.
2. Description of the Related Art
Forging processes, such as pressing or the like, sometimes suffer from defects, such as forging defects, dead metal, buckling or the like, depending on the combination of whether the workability of a material is good and how the material is processed. To analyze such defects, a fiber flow line is conventionally observed. Observation of a fiber flow line makes it possible to identify the type of the defect and detect the condition of friction between the workpiece and a die. In order to observe a fiber flow line, however, it is necessary to prepare a die, forge a material with the die, cut out a sample piece for the observation from the forged material, grind and etch the sample piece, and place it under a microscope. Results of the observation are fed back to the die designing or the production process designing. A single cycle of this procedure of observation and feedback consumes a long period of time, for example, several months. Therefore, the process designing cannot be quickly accomplished.
To avoid consumption of a long time, computer simulation of a forging process is often employed to predict the state of a fiber flow line occurring after the process. In many cases, such a simulation is performed by a finite element method. In a conventional manner of simulation based on the finite element method, a workpiece is divided into many elements by setting a grid mesh in the workpiece, and the displacements of individual element-forming nodes (grid points) are sequentially calculated to simulate the deformation of the entire workpiece.
However, the aforementioned conventional arts have the following problems. That is, the method in which a fiber flow line in an actually processed material is observed consumes an inconveniently long time as mentioned above. Furthermore, the method does not allow observation of material flowage in a cross section of a sample piece perpendicular to the length of the piece because a fiber flow line does not exist in such a section.
The conventional manner of computer simulation of a forging process is not able to provide a result whose fineness exceeds the fineness of the grid mesh set during an initial period of the analysis. This problem becomes remarkable particularly at sites of a workpiece that have high rates of surface area expansion. Furthermore, at a position between nodes, a left-behind phenomenon in which a deformed portion is left behind in a die sometimes occurs. This phenomenon makes it impossible to simulate a precise shape occurring after deformation.
Accordingly, the invention is intended to solve the aforementioned problems of the conventional technologies for analyzing a forging process. It is an object of the invention to provide a forging process analyzing method that allows simulation of a forging process within a short period of time, and also allows high-precision analysis with respect to a section perpendicular to the length of a workpiece and a site of a great expansion, and further allows display of results of the analysis in a three-dimensional manner, and to provide a medium storing a program for executing the method.
In the forging process analyzing method of the invention, a plurality of trace points for expressing at least one fiber flow line are set in a workpiece that is to be forged by a die. Furthermore, a displacement of each trace point involved in deformation of the workpiece is calculated. At least one post-deformation fiber flow line is expressed in the workpiece by connecting the trace points after displacement.
More specifically, trace points are set in the shape of a workpiece before a process is performed on the workpiece. The trace points provided for expressing fiber flow lines. That is, a bent or curved line obtained by connecting trace points expresses a fiber flow line. Arbitrary fiber flow lines can be set. That is, the fiber flow lines may be lines that match real fiber flow caused by the past processes actually performed on a workpiece or lines based on a simulation of real fiber flow. Furthermore, the fiber flow lines may also be imaginary lines that are irrelevant to real fiber flow. With regard to each trace point, a displacement involved in deformation caused by a process performed on the workpiece is calculated. Normally, this calculation is executed by iterative operation. Then, the post-displacement trace points are connected to form bent or curved lines that express fiber flow lines occurring after the workpiece has been processed.
Based on the post-process fiber flow lines, it is possible to predict whether the workability is good when the workpiece is actually subjected to the forging process. That is, it is possible to predict a possibility of occurrence of defects, such as a forging defect, dead metal, buckling and the like. This forging process analyzing method can be performed through computer processing. The computation time required by the method is only slightly longer than the computation time required when a normal finite element method is employed. Therefore, results of the analysis can be fed back to the die designing and the production process designing in a turn-around time of only one day or less. The forging process analyzing method thus contributes to quick process designing. Furthermore, the method of the invention achieves finer and closer results than a method in which fiber flow lines are formed by using element-forming nodes.
The forging process analyzing method of the invention is intended for the application to an analysis based on a Lagrangian method in which trace points are not fixed in a space but set as mobile points that move together with a workpiece material and the movement of the trace points caused by a workpiece process is tracked. Therefore, it is not essential to place trace points on a surface of a workpiece during the setting of trace points. Trace points belong to the same elements before and after being displaced.
In the forging process analyzing method of the invention, a new trace point may be set between trace points in a portion that has a high rate of expansion caused by deformation. That is, when calculation of a displacement of each trace point finds that the distance between post-displacement trace points has become equal to or greater than a certain value, a new trace point is set between those trace points. Then, the subsequent calculating process is performed. Therefore, it becomes possible to perform fine and close analysis even at a site of a high rate of expansion caused by the workpiece process (typically interpreted as a high rate of expansion of surface area).
The additional setting of a new trace point may be performed in the following manner. That is, a distance between adjacent trace points present on a fiber flow line is compared with a predetermined critical value. When the distance between the adjacent trace points exceeds the critical value, a new trace point is set. This manner of setting a new trace point prevents the distance between trace points from exceeding the critical value even at a site of expansion caused by deformation. Therefore, it becomes possible to perform fine and close analysis even at a site of a high expansion rate.
Furthermore, in the forging process analyzing method of the invention, when there is a trace point that is to be left behind in a die due to deformation, an element containing the trace point may be converted into a correction element in which an element side extending in a shape of the die is replaced by a line expressing the shape of the die. Through conversion of the element, positions of all trace points present in the element that contains the trace point that would otherwise be left behind can be corrected by an interpolating process. This processing manner makes it possible to perform high-precision analysis even in a portion where a normal finite element method would cause a trace point to be left behind in the die or cause fiber flow lines to cross each other, and therefore would suffer form a remarkable reduction of analysis precision.
Prevention of such a left-behind phenomenon may be performed as follows. When a die shape-expressing line extends in an outermost peripheral element of a workpiece, it is determined that a trace point contained in the outermost peripheral element is likely to be left behind in the die. Then, a process for preventing the left-behind phenomenon is performed with respect to the trace points contained in the element. That is, the aforementioned conversion is performed on the element, and the positions of all the trace points present in the element are corrected.
In the forging process analyzing method of the invention, it is also possible to set trace points so as to express fiber flow lines in a section that intersects with the length of a workpiece and, in particular, a section perpendicular to the length of the workpiece. In the case of a material prepared in a normal shape, such as a billet or a platy material or the like, the aforementioned section does not have fiber flow in reality. Therefore, the behavior of deformation in such a section cannot easily be analyzed by a method in which a test sample is polished and etched and then observed. However, since the forging process analyzing method of the invention is able to analyze imaginary fiber flow lines, the method can analyze fiber flow lines in a section intersecting with the length of a workpiece. That is, the method can also analyze fiber flow lines expressed by trace points set in the aforementioned manner. Therefore, it becomes possible to predict a condition of migration of the material in a section that interests with the length of the workpiece.
Furthermore, in the forging process analyzing method of the invention, a fiber flow line having a thickness may be expressed by providing post-displacement trace points with radii. As a result, each fiber flow line is expressed not as a mere point but as a finite area even during the observation of a section that intersects with the post-deformation fiber flow lines. Therefore, when three-dimensional consideration is to be performed on results of the analysis, the behavior of fiber flow lines can easily be understood in an arbitrarily selected section. This technique is particularly useful when trace points are set by simulating real fiber flow lines.
When such a three-dimensional analysis is to be performed, the radius of a trace point should be adjusted because after the workpiece is deformed, a trace point may possibly be located close to a surface of the workpiece or may be located close to another trace point. When in such cases, equal radii are provided for all the trace points, a fiber flow line containing a trace point adjacent to a surface of the workpiece will likely extend out of the boundary of the workpiece in the former case. In the latter case, adjacent fiber flow lines will likely overlap each other. Neither the off-boundary extension nor the overlap of fiber flow lines can occur in reality since fiber flow lines do not have a thickness in a real workpiece.
Therefore, when there is a fiber flow line extending off the boundary of a workpiece, the radius of the fiber flow line should be adjusted so that the fiber flow line is contained inside the boundary of the workpiece. When fiber flow lines overlap each other, the radius adjustment should be performed so that the overlap is eliminated. In either case, the radius adjustment is performed in the reducing direction. The radius adjustment for the aforementioned purposes may be applied collectively to all the trace points, or may also be applied individually to only the trace points having a specific problem as mentioned above. It should be noted that the latter manner of radius adjustment is more advantageous because larger radii of fiber flow lines make an easier-to-see display of results of the analysis.
When the trace points are provided with radii in this invention, it is useful to provide a display picture in which the interior of each fiber flow line is filled in in a section of the workpiece after the workpiece has been deformed. In such a display, the condition of congregation of fiber flow lines can be grasped based on the degree of sparsity or density of the filled-in portions. Furthermore, based on the shape of a filled-in portion (whether it is circular or elliptical), the intersecting angle of the fiber flow line to which the filled-in portion belongs with respect to the sectional face can be estimated. Therefore, it becomes possible to perform further detailed or three-dimensional consideration on results of the analysis.
The mechanically readable medium of the invention stores a program for causing a computer to execute the above-described procedures of the forging process analyzing method of the invention. Using the mechanically readable medium, it becomes possible to cause a computer to execute the forging process analyzing method of the invention.